{
  "id": "2205.06795",
  "version": "v1",
  "published": "2022-05-13T17:41:50.000Z",
  "updated": "2022-05-13T17:41:50.000Z",
  "title": "On degenerate blow-up profiles for the subcritical semilinear heat equation",
  "authors": [
    "Frank Merle",
    "Hatem Zaag"
  ],
  "comment": "61 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the semilinear heat equation with a superlinear power nonlinearity in the Sobolev subcritical range. We construct a solution which blows up in finite time only at the origin, with a completely new blow-up profile, which is cross-shaped. Our method is general and extends to the construction of other solutions blowing up only at the origin, with a large variety of blow-up profiles, degenerate or not.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-13T17:41:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L05",
      "35K10",
      "35K58",
      "35B44",
      "35B40"
    ],
    "keywords": [
      "subcritical semilinear heat equation",
      "degenerate blow-up profiles",
      "superlinear power nonlinearity",
      "sobolev subcritical range",
      "finite time"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 61,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}